
on Game Theory 
Issue of 2012‒09‒09
twentytwo papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University 
By:  Christoph Kuzmics; Thomas Palfrey; Brian Rogers 
Abstract:  We study symmetric play in a class of repeated games when players are patient. We show that, while the use of symmetric strategy profiles essentially does not restrict the set of feasible payoffs, the set of equilibrium payoffs is an interesting proper subset of the feasible and individually rational set. We also provide a theory of how rational individuals play these games, identifying particular strategies as focal through the considerations of Pareto optimality and simplicity. We report experiments that support many aspects of this theory. JEL Code: C73, C92, D63 
Keywords:  symmetry, repeated games, focal points, experiments 
Date:  2012–07–01 
URL:  http://d.repec.org/n?u=RePEc:nwu:cmsems:1551&r=gth 
By:  Casajus, André; Hüttner, Frank 
Abstract:  The Shapley value certainly is the most eminent singlepoint solution concept for TUgames. In its standard characterization, the null player property indicates the absence of solidarity among the players. First, we replace the null player property by a new axiom that guarantees null players nonnegative payoffs whenever the grand coalition's worth is nonnegative. Second, the equal treatment property is strengthened into desirability. This way, we obtain a new characterization of the class of egalitarian Shapley values, i.e., of convex combinations of the Shapley value and the equal division solution. We complement this result by characterizations of the class of generalized consensus values, i.e., of convex combinations of the Shapley value and the equal surplus division solution.  
Keywords:  Solidarity,egalitarian Shapley value,equal division value,desirability,generalized consensus value 
JEL:  C71 D60 
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:zbw:leiwps:113&r=gth 
By:  J Arin (Dpto. Ftos. A. Económico I, University of the Basque Country); V Feltkamp (Maastricht School of Management); M Montero (School of Economics, University of Nottingham) 
Abstract:  This paper studies a noncooperative allocation procedure for coali tional games with veto players. The procedure is similar to the one presented by Dagan et al. (1997) for bankruptcy problems. According to it, a player, the proposer, makes a proposal that the remaining players must accept or reject. We present a model where the proposer can make sequential proposals over n periods. If responders are myopic maximizers (i.e. consider each period in isolation), the only subgame perfect equilibrium outcome is the serial rule of Arin and Feltkamp (2012) regardless of the order of moves. If all players are rational, the serial rule still arises as the unique subgame perfect equilibrium out come if the order of moves is such that stronger players must respond to the proposal after weaker ones. 
Keywords:  veto players, noncooperative bargaining, myopic behavior, serial rule 
Date:  2012–11 
URL:  http://d.repec.org/n?u=RePEc:not:notcdx:201211&r=gth 
By:  László Á. Kóczy (Óbuda University) 
Abstract:  We study coalitional games where the coalitional payoffs depend on the entire coalition structure. We introduce a noncooperative, sequential coalition formation model and show that the set of equilibrium outcomes coincides with the recursive core, a generalisation of the core to such games. In order to extend past results limited to totally recursivebalanced partition function form games we introduce subgameconsistency that requires perfectness in relevant subgames only, while some unreached subgames are ignored. Due to the externalities, the profitability of deviations depends on the partition formed by the remaining players: the stability of core payoff configurations is ensured by a combination of the pessimism of players going for certain profits only and the assumption that players base their stationary strategies on a madeup history punishing some of the possible deviators  and getting this sometimes right. 
Keywords:  partition function, externalities, implementation, recursive core, stationary perfect equilibrium, time consistent equilibrium JEL Codes: C71, C72 
Date:  2012–08 
URL:  http://d.repec.org/n?u=RePEc:pkk:wpaper:1203&r=gth 
By:  Maria Montero (School of Economics, University of Nottingham); Juan VidalPuga (Faculty of Economics and Management, Universidade de Vigo) 
Abstract:  A power measure is monotone if a player with a larger weight is assigned at least as much power as a player with a smaller weight in the same weighted majority game. Failure of a power index to satisfy monotonicity is often considered a pathological feature. In this paper, we show that monotonicity may fail in the unique subgame perfect equilibrium of a noncooperative bargaining game. A player with a smaller weight may have a higher expected payoff than a player with a larger weight. This is possible even though coalition formation and payoff division are endogenous, all players are rational and there is no asymmetry between the players other than in the weights. 
Keywords:  monotonicity, noncoopeative 
Date:  2012–04 
URL:  http://d.repec.org/n?u=RePEc:not:notcdx:201204&r=gth 
By:  Daniele Nosenzo (School of Economics, University of Nottingham); Theo Offerman (CREED, Department of Economics, University of Amsterdam); Martin Sefton (School of Economics, University of Nottingham); Ailko van der Veen (CBESS, School of Economics, University of East Anglia) 
Abstract:  We experimentally investigate a repeated “inspection game” where, in the stage game, an employee can either work or shirk and an employer simultaneously chooses to inspect or not inspect. Combined payoffs are maximized when the employee works and the employer does not inspect. However, the unique equilibrium of the stage game is in mixed strategies with positive probabilities of shirking/inspecting. We examine the effects of allowing the employer to sanction or reward the employee after she has inspected the employee. We find that rewards or sanctions can both discourage shirking, and have similar effects on joint earnings. In games allowing sanctions a reduction in shirking is accomplished with a lower inspection rate and the efficiency gains accrue to employers. In games allowing rewards employers actively reward employees for working and the efficiency gains are shared more equitably. A treatment where employers can combine sanctions and rewards leads to efficiencies similar to the singleinstrument treatments, and outcomes more closely resemble those of the reward treatment in that the efficiency gains are shared. 
Keywords:  inspection game, costly monitoring, discretionary incentives, rewards, punishment, experiment 
Date:  2012–10 
URL:  http://d.repec.org/n?u=RePEc:not:notcdx:201210&r=gth 
By:  Alex Possajennikov (School of Economics, University of Nottingham) 
Abstract:  Using belief elicitation, the paper investigates the formation and the evolution of beliefs in a signalling game in which a common prior on Sender's type is not induced. Beliefs are elicited about the type of the Sender and about the strategies of the players. The experimental subjects often start with diuse uniform beliefs and update them in view of observations. However, the speed of updating is in uenced by the strength of the initial beliefs. An interesting result is that beliefs about strategies are updated faster than beliefs about types. In the medium run, for some specications of game parameters, this leads to outcomes being signicantly dierent from the outcomes of the game in which a common prior is induced. It is also shown that elicitation of beliefs does not considerably change the pattern of play. 
Keywords:  beliefs,signalling,experiment,learning,belief elicitation 
Date:  2012–06 
URL:  http://d.repec.org/n?u=RePEc:not:notcdx:201206&r=gth 
By:  Andrew Monaco (Department of Economics, University of Kansas); Tarun Sabarwal (Department of Economics, University of Kansas) 
Abstract:  This paper analyzes games with both strategic substitutes and strategic complements. Such games may behave differently from either games with strategic complements or games with strategic substitutes. In such games, equilibria do not decrease as the parameter increases. Moreover, natural conditions are presented to guarantee that an increase in the parameter leads to an increase in the equilibrium: in other words, conditions to guarantee monotone comparative statics. These conditions are based on intuitive tradeoffs between direct parameter effects and indirect strategic effects. These conditions are needed only for players with strategic substitutes; no conditions are imposed on players with strategic complements. Several examples highlight the results. 
Keywords:  Lattice games, strategic complements, strategic substitutes, equilibrium set, monotone comparative statics 
JEL:  C70 C72 
Date:  2012–08 
URL:  http://d.repec.org/n?u=RePEc:kan:wpaper:201236&r=gth 
By:  Qingmin Liu (Department of Economics, Columbia University); George J. Mailath (Department of Economics, University of Pennsylvania); Andrew Postlewaite (Department of Economics, University of Pennsylvania); Larry Samuelson (Department of Economics, Yale University) 
Abstract:  A large literature uses matching models to analyze markets with twosided heterogeneity, studying problems such as the matching of students to schools, residents to hospitals, husbands to wives, and workers to firms. The analysis typically assumes that the agents have complete information, and examines core outcomes. We formulate a notion of stable outcomes in matching problems with onesided asymmetric information. The key conceptual problem is to formulate a notion of a blocking pair that takes account of the inferences that the uninformed agent might make from the hypothesis that the current allocation is stable. We show that the set of stable outcomes is nonempty in incomplete information environments, and is a superset of the set of completeinformation stable outcomes. We provide sufficient conditions for incompleteinformation stable matchings to be efficient. 
Keywords:  Matching, Stability, Stable outcome, Incomplete information, Core 
JEL:  C71 C78 D5 D 
Date:  2012–08–26 
URL:  http://d.repec.org/n?u=RePEc:pen:papers:12032&r=gth 
By:  Takuya Masuzawa (Faculty of Economics, Keio University) 
Abstract:  We describe the mechanism of feedback methods of counting single transferable votes, such as Meek's method, in the framework of nperson strategic games. We show that the games are in the class introduced by Masuzawa (International Journal of Game Theory 32:2003 and 37:2008), and that for any given finite domain of keep value, the algorithm by Masuzawa (2008) correctly maximizes the set of winners and minimizes the corresponding keep values. Starting at zero, our algorithm increases the keep value of any candidate until the surplus becomes positive, while the prevailing method decreases it and does not necessarily attain the maximum set of winners. 
Date:  2012–08 
URL:  http://d.repec.org/n?u=RePEc:kei:dpaper:2012015&r=gth 
By:  Grimalday, Gianluca (Universitat Jaume I); Karz, Anirban (Delhi School of Economics, University of Delhi); Proto, Eugenio (University of Warwick) 
Abstract:  Fairness emerges as a relevant factor in redistributive preferences in surveys and experiments. We study experimentally the impact of varying the probability with which players are assigned to initial positions in Ultimatum Games (UGs). In the baseline case players have equal opportunities of being assigned the proposer position ñ arguably the more advantaged one in UGs. Chances become increasingly unequal across three treatments. We also manipulate the intertemporal allocation of opportunities over rounds. We Önd that: (1) The more initial chances are distributed unequally, the lower the acceptance rates of a given o§er; consequently, o§ers increase; (2) Being assigned a mere 1% chance of occupying the proposer role compared to none, significantly increases acceptance rates and decreases o§ers; (3) Players accept even extreme amounts of unequal chances within each round in exchange for overall equality of opportunities across rounds. Procedural fairness both static and dynamic  has clear relevance for individuals. 
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:cge:warwcg:92&r=gth 
By:  Vincent Anesi (School of Economics, University of Nottingham); Daniel J Seidmann (School of Economics, University of Nottingham) 
Abstract:  We present a model of bargaining in which a committee searches over the policy space, successively amending the default by voting over proposals. Bargaining ends when proposers are unable or unwilling to amend the existing default, which is then implemented. We characterize the policies which can be implemented from any initial default in a pure strategy stationary Markov perfect equilibrium for an interesting class of environments including multidimensional and infinite policy spaces. Minimumwinning coalitions may not form, and a player who does not propose may nevertheless earn all of the surplus from agreement. The set of immovable policies (which are implemented, once reached as default) forms a weakly stable set; and conversely, any weakly stable set is supported by some equilibrium. If the policy space is well ordered then the committee implements the ideal policy of the last proposer in a subset of a weakly stable set. However, this result does not generalize to other cases, allowing us to explore the effects of protocol manipulation. Variations in the quota and in the set of proposers may have surprising effects on the set of immovable policies. We also show that equilibria of our model are contemporaneous perfect eequilibria of a related model of repeated implementation with an evolving default; and that immovable policies in semiMarkovian equilibria form the largest consistent set. 
Keywords:  bargaining, committee voting, evolving default, stable set 
Date:  2012–03 
URL:  http://d.repec.org/n?u=RePEc:not:notcdx:201203&r=gth 
By:  Vincent Anesi (School of Economics, University of Nottingham); Daniel J Seidmann (School of Economics, University of Nottingham) 
Abstract:  Committee voting has mostly been investigated from the perspective of the standard BaronFerejohn model of bargaining over the division of a pie, in which bargaining ends as soon as the committee reaches an agreement. In standing committees, however, existing agreements can be amended. This paper studies an extension of the BaronFerejohn framework to a model with an evolving default that reflects this important feature of policymaking in standing committees: In each of an infinite number of periods, the ongoing default can be amended to a new policy (which in turn determines the default for the next period). The model provides a number of quite different predictions. In particular: (i) Substantial shares of the pie are wasted each period and the size principle fails in some pure strategy Markov perfect equilibria of nonunanimity games with patient enough players; and (ii) All Markov perfect equilibria are Pareto inefficient when discount factors are heterogenous. However, there is a unique equilibrium outcome in unanimity standing committee games, which coincides with the unique equilibrium outcome of the corresponding BaronFerejohn framework. 
Keywords:  legislative bargaining, endogenous default, efficiency, pork barrel 
Date:  2012–09 
URL:  http://d.repec.org/n?u=RePEc:not:notcdx:201209&r=gth 
By:  Franz Hubert (Humboldt–Universitat zu Berlin); Onur Cobanli (Humboldt–Universitat zu Berlin) 
Abstract:  We use cooperative game theory to analyze the impact of three controversial pipeline projects on the power structure in the Eurasian trade of natural gas. Two of them, Nord Stream and South Stream, allow Russian gas to bypass transit countries, Ukraine and Belarus. Nord Stream’s strategic value turns out to be huge, justifying the high investment cost for Germany and Russia. The additional leverage obtained through South Stream, in contrast, appears small. The third project, Nabucco, aims at diversifying Europe’s gas imports by accessing producers in Middle East and Central Asia. It curtails Russia’s power, but the benefits accrue mainly to Turkey, while the gains for the EU are negligible. 
Keywords:  Bargaining Power, Network, Trade links, Natural Gas 
JEL:  L5 L9 O22 
Date:  2012–09 
URL:  http://d.repec.org/n?u=RePEc:koc:wpaper:1224&r=gth 
By:  Busetto, Francesca (Dipartimento di Scienze Economiche e Statistiche, Universitµ a degli Studi di Udine); Codognato, Giulio (Dipartimento di Scienze Economiche e Statistiche, Universitµ a degli Studi di Udine); Ghosal, Sayantan (Department of Economics, University of Warwick) 
Abstract:  In this paper, in an exchange economy with atoms and an atomless part, we analyze the relationship between the set of the CournotNash equilibrium allocations of a strategic market game and the set of the Walras equilibrium allocations of the exchange economy with which it is associated. In an example, we show that, even when atoms are countably infinite, CournotNash equilibria yield different allocations from the Walras equilibrium allocations of the underlying exchange economy. We partially replicate the exchange economy by increasing the number of atoms without affecting the atomless part while ensuring that the measure space of agents remains ¯nite. We show that any sequence of CournotNash equilibrium allocations of the strategic market game associated with the partially replicated exchange economies approximates a Walras equilibrium allocation of the original exchange economy. JEL classification: 
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:wrk:warwec:994&r=gth 
By:  Aviad Heifetz; Willemien Kets 
Abstract:  This paper constructs a type space that contains all types with a finite depth of reasoning, as well as all types with an infinite depth of reasoning  in particular those types for whom finitedepth types are conceivable, or think that infnitedepth types are conceivable in the mind of other players, etcetera. We prove that this type space is uni versal with respect to the class of type spaces that include types with a finite or infinite depth of reasoning. In particular, we show that it contains the standard universal type space of Mertens and Zamir (1985) as a beliefclosed subspace, and that this subspace is characterized by common belief of infinitedepth reasoning. This framework allows us to study the robustness of classical results to small deviations from perfect rationality. As an example, we demonstrate that in the global games of Carlsson and van Damme (1993), a small ‘grain of naivete’ suffices to overturn the classical uniqueness results in that literature. JEL Code: C700, C720, D800, D830 
Keywords:  Levelk models, cognitive hierarchy models, universal type space, global games 
Date:  2012–08–04 
URL:  http://d.repec.org/n?u=RePEc:nwu:cmsems:1550&r=gth 
By:  Andrea Galeotti; Brian Rogers 
Abstract:  We consider the spread of a harmful state through a population divided into two groups. Interaction patterns capture the full spectrum of assortativity possibilities. We show that a central planner who aims for eradication optimally either divides equally the resources across groups, or concentrates entirely on one group, depending on whether there is positive or negative assortativity, respectively. We study a game in which agents can, at a cost, immunize. Negative assortative interactions generate highly asymmetric equilibrium outcomes between exante identical groups. When groups have an underlying dierence, even a small amount of intergroup contacts generates large asymmetries. JEL Code: D61, H51, i14 
Keywords:  Diffusion, SIS, externalities 
Date:  2012–07–26 
URL:  http://d.repec.org/n?u=RePEc:nwu:cmsems:1552&r=gth 
By:  CostaGomes, Miguel A.; Huck, Steffen; Weizsäcker, Georg 
Abstract:  In many economic contexts, an elusive variable of interest is the agent's belief about relevant events, e.g. about other agents' behavior. A growing number of surveys and experiments ask participants to state beliefs explicitly but little is known about the causal relation between beliefs and other behavioral variables. This paper discusses the possibility of creating exogenous instrumental variables for belief statements, by informing the agent about exogenous manipulations of the relevant events. We conduct trust game experiments where the amount sent back by the second player (trustee) is exogenously varied. The procedure allows detecting causal links from beliefs to actions under plausible assumptions. The IVestimated effect is significant, confirming the causal role of beliefs. It is only slightly and insignificantly smaller than in estimations without instrumentation, consistent with a mild effect of social norms or other omitted variables.  In vielen ökonomischen Zusammenhängen sind die Erwartungen der Spieler bezüglich relevanter Ereignisse, z. B. über das Verhalten anderer Spieler, eine schwer zu fassende Variable von Interesse. Zwar werden in einer wachsenden Zahl von Untersuchungen und Experimenten Teilnehmer gebeten, ihre Erwartungen ausdrücklich zu nennen, jedoch ist noch wenig bekannt über die Kausalbeziehung zwischen Erwartungen und anderen Verhaltensvariablen. In diesem Paper wird die Möglichkeit diskutiert, Instrumente zur Erhebung von Erwartungen zu kreieren, bei denen der Spieler über exogene Manipulationen der relevanten Ereignisse informiert wird. Wir führen Experimente zu einem Vertrauensspiel durch, bei denen der Betrag, der durch den zweiten Spieler zurückgesendet wird (trustee), exogen variiert wird. Dieses Vorgehen erlaubt die Entdeckung kausaler Wirkungsketten von Erwartungen auf Entscheidungen unter plausiblen Annahmen. Der IVgeschätzte Effekt ist signifikant und bestätigt die kausale Rolle von Erwartungen. Er ist nur wenig kleiner als in Schätzungen ohne Instrumentation und konsistent mit einem leichten Effekt sozialer Normen oder anderen vernachlässigter Variablen. 
Keywords:  Social Capital,trust game,instrumental variables,belief elicitation 
JEL:  C72 C81 C91 D84 
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:zbw:wzbeoc:spii2012302&r=gth 
By:  Ulrike Vollstädt (Jena Graduate School "Human Behaviour in Social and Economic Change", University of Jena); Robert Böhm (Center for Empirical Research in Economics and Behavioral Scienes (CEREB), University of Erfurt) 
Abstract:  In reality, it is often groups rather than individuals that make decisions. In previous experiments, groups have frequently been shown to act differently from individuals in several ways. It has been claimed that intergroup interactions may be (1) more competitive, (2) more rational, or (3) more prosocial than interindividual interactions. While some of these observed differences may be due to differences in the experimental designs, it is still not clear which of the three motivations is prevailing as they have often been behaviorally confounded in previous experiments. We use Rubinstein's alternating offers bargaining game to compare interindividual with intergroup behavior since it allows separating the predictions of competitive, rational and prosocial behavior. We find that groups are, on average, more rational bargainers than individuals. 
Keywords:  alternating offers bargaining experiment, intergroup behavior, interindividual behavior 
JEL:  C78 D70 
Date:  2012–08–23 
URL:  http://d.repec.org/n?u=RePEc:jrp:jrpwrp:2012048&r=gth 
By:  Stracke, Rudi; Kerschbamer, Rudolf; Sunde, Uwe 
Abstract:  This paper analyzes a twostage pairwise elimination contest with heterogeneous agents. It derives analytical expressions for equilibrium efforts in a setting where the two simultaneous stage1 interactions are linked through endogenously determined continuation values. 
Keywords:  MultiStage Elimination Contest; Heterogeneity; Endogenous Continuation Value 
JEL:  C72 D72 J33 
Date:  2012–08 
URL:  http://d.repec.org/n?u=RePEc:usg:econwp:2012:20&r=gth 
By:  Pradeep Dubey (Department of Economics, Stony Brook University); Siddhartha Sah (Department of Mathematics, Rutgers University, New Brunswick, New Jersey) 
Abstract:  Consider agents who undertake costly effort to produce stochastic outputs observable by a principal. The principal can award a prize deterministically to the agent with the highest output, or to all of them with probabilities that are proportional to their outputs. We show that, if there is sufficient diversity in agents' skills relative to the noise on output, then the proportional prize will, in a precise sense, elicit more output on average, than the deterministic prize. Indeed, assuming agents know each others?skills (the complete information case), this result holds when any Nash equilibrium selection, under the proportional prize, is compared with any individually rational selection under the deterministic prize. When there is incomplete information, the result is still true but now we must restrict to Nash selections for both prizes. We also compute the optimal scheme, from among a natural class of probabilistic schemes, for awarding the prize; namely that which elicits maximal effort from the agents for the least prize. In general the optimal scheme is a monotonic step function which lies ?between?the proportional and deterministic schemes. When the competition is over small fractional increments, as happens in the presence of strong contestants whose base levels of production are high, the optimal scheme awards the prize according to the "log of the odds", with odds based upon the proportional prize. 
JEL:  C70 C72 C79 D44 D63 D82 
Date:  2012–03 
URL:  http://d.repec.org/n?u=RePEc:nys:sunysb:1202&r=gth 
By:  Alistair Wilson 
Abstract:  I develop a novel model of groupbased deliberation in which communication is costly in two directions: agents must pay separate costs to send and to receive messages. Equilibrium strategies have an intuitive characterization  those with the best information send, those with the worst information receive. But freeriding leads to less information exchange than is optimal. Testing the model`s predictions with an experiment I find that subjects overcommunicate when costs are high, but fail to benefit from this as much as they should. In welfare terms the experiment finds that listening costs are more harmful to welfare, in contrast with theory, which indicates sending costs. The experiment also suggests that the existence of costly communication channels can reduce total welfare. 
Keywords:  Group Communication, Information transmission, Information public goods 
JEL:  C72 C92 D83 D84 
Date:  2012–06 
URL:  http://d.repec.org/n?u=RePEc:pit:wpaper:499&r=gth 